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Warm-Up: March 18, 2013

Warm-Up: March 18, 2013. Solve for P(t):. Homework Questions?. Population Growth. Section 6.5. Exponential Population Growth Model. Many populations grow at a rate proportional to the size of the population. where k is the relative growth rate . The resulting exponential growth model is

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Warm-Up: March 18, 2013

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  1. Warm-Up: March 18, 2013 • Solve for P(t):

  2. Homework Questions?

  3. Population Growth Section 6.5

  4. Exponential Population Growth Model • Many populations grow at a rate proportional to the size of the population. • where k is the relative growth rate. • The resulting exponential growth model is • We usually use t=0 as the first year of our model

  5. Example 1 • Springfield has a current population of 36000 and is growing at a relative rate of 2.3%. • Write a differential equation for the population. • Find a formula for the population P(t). • Superimpose the graph of the population function on a slope field for the differential equation.

  6. Logistic Population Growth Model • Populations cannot increase forever. • Environmental factors often limit the population to some maximum value, M, called the carrying capacity. • The logistic growth model is found from the following logistic differential equation:

  7. Example 2 • Find k and the carrying capacity for the population represented by

  8. Logistic Growth Model • The solution to • Is given by • Where A is a constant found using the given initial condition

  9. Assignment • Read Section 6.5 (pages 342-346) • Page 347 Exercises #1-15 odd • Read Section 6.6 (pages 350-355)

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